Localization may survive in periodically driven (Floquet) quantum systems, but is generally unstable for aperiodic drives. In this work we identify a disordered spin-1 2 XX chain driven quasi-periodically via a Thue-Morse sequence as a system exhibiting persistent localization under aperiodic driving. The stability is underpinned by a hidden conservation law originating from a chiral symmetry. Therefore, rather counter-intuitively, adding further potential disorder delocalizes the system, via an exceptionally long-lived prethermal regime. This provides a first example of persistent 'localization without eigenstates'.